BGBiogeosciencesBGBiogeosciences1726-4189Copernicus GmbHGöttingen, Germany10.5194/bg-12-3993-2015Scaling impacts on environmental controls and spatial heterogeneity of soil organic carbon stocksMishraU.umishra@anl.govRileyW. J.https://orcid.org/0000-0002-4615-2304Environmental Science Division, Argonne National Laboratory, 9700
South Cass Avenue, 240-6143, Argonne, IL 60439, USAEarth Sciences Division, Lawrence Berkeley National Laboratory, One
Cyclotron Road, 50-4037, Berkeley, CA 94720, USAU. Mishra (umishra@anl.gov)02July201512133993400424November201427January201502June201511June2015This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://bg.copernicus.org/articles/12/3993/2015/bg-12-3993-2015.htmlThe full text article is available as a PDF file from https://bg.copernicus.org/articles/12/3993/2015/bg-12-3993-2015.pdf
The spatial heterogeneity of land surfaces affects energy, moisture, and
greenhouse gas exchanges with the atmosphere. However, representing the
heterogeneity of terrestrial hydrological and biogeochemical processes in
Earth system models (ESMs) remains a critical scientific challenge. We
report the impact of spatial scaling on environmental controls, spatial
structure, and statistical properties of soil organic carbon (SOC) stocks
across the US state of Alaska. We used soil profile observations and
environmental factors such as topography, climate, land cover types, and
surficial geology to predict the SOC stocks at a 50 m spatial scale.
These spatially heterogeneous estimates provide a data set with reasonable
fidelity to the observations at a sufficiently high resolution to examine
the environmental controls on the spatial structure of SOC stocks. We
upscaled both the predicted SOC stocks and environmental variables from
finer to coarser spatial scales (s= 100, 200, and 500 m and 1, 2, 5, and
10 km) and generated various statistical properties of SOC stock estimates.
We found different environmental factors to be statistically significant
predictors at different spatial scales. Only elevation, temperature,
potential evapotranspiration, and scrub land cover types were significant
predictors at all scales. The strengths of control (the median value of
geographically weighted regression coefficients) of these four environmental
variables on SOC stocks decreased with increasing scale and were accurately
represented using mathematical functions (R2= 0.83–0.97). The spatial
structure of SOC stocks across Alaska changed with spatial scale. Although
the variance (sill) and unstructured variability (nugget) of the calculated
variograms of SOC stocks decreased exponentially with scale, the correlation
length (range) remained relatively constant across scale. The variance of
predicted SOC stocks decreased with spatial scale over the range of 50 m to
∼ 500 m, and remained constant beyond this scale. The fitted
exponential function accounted for 98 % of variability in the variance of
SOC stocks. We found moderately accurate linear relationships between mean
and higher-order moments of predicted SOC stocks (R2∼ 0.55–0.63).
Current ESMs operate at coarse spatial scales (50–100 km), and
are therefore unable to represent environmental controllers and spatial
heterogeneity of high-latitude SOC stocks consistent with observations. We
conclude that improved understanding of the scaling behavior of
environmental controls and statistical properties of SOC stocks could
improve ESM land model benchmarking and perhaps allow representation of
spatial heterogeneity of biogeochemistry at scales finer than those
currently resolved by ESMs.
Introduction
Soil organic carbon (SOC) stocks have large spatial heterogeneity globally
(Todd-Brown et al., 2013) and in the northern circumpolar permafrost region
(Ping, 2013; Hugelius et al., 2014). Achieving an accurate representation of
the spatial heterogeneity of existing SOC stocks in Earth system models
(ESMs) is a prerequisite for predicting future carbon–climate feedbacks
(Todd-Brown et al., 2013), given that uncertainty resulting from the
distribution of SOC stocks accounts for a large proportion of the overall
uncertainty (Burke et al., 2012) in predictions of future greenhouse gas
concentrations and associated climate changes. Reliable estimates of
regional SOC stocks and their spatial heterogeneity are also essential to
gaining a better understanding of existing environmental controls of SOC
stocks and their vulnerability to changing climate (Johnson et al., 2011).
At present, large differences exist between observation-based and ESM-based
SOC stock estimates at high latitudes (Mishra et al., 2013). Several factors
likely account for these differences (Koven et al., 2013; Todd-Brown et al.,
2013); the relevant factors for the current analyses are that the natural
spatial variability of some environmental controls observed to affect SOC
stocks are not represented in the models. One potential approach to account
for spatial heterogeneity in ESMs is to incorporate the impacts of
environmental controls on SOC stocks at a spatial scale consistent with the
observations.
Among environmental variables, climate, topography, organisms, parent
material, time, and spatial position (Jenny, 1941; McBratney et al., 2003)
have widely been used to predict the spatial variability of soil properties
from plot to regional scales (Thompson and Kolka; 2005; Vasques et al.,
2012; Minasny et al., 2013; Mishra and Riley, 2014). At high latitudes where
solar radiation and evaporation are strongly related to the geometry of the
land surface (McKenzie et al., 2000), topography has been reported to play
an important role in determining the level of SOC at a specific location
(Jenny, 1980; Birkeland, 1984; Hobbie et al., 2000). Hill slope processes,
such as erosion and deposition, are related to terrain attributes, such as
the soil wetness index (SWI) and sediment transport index (STI). Both the
SWI and STI are strong predictors of SOC stocks and have been used
extensively in digital mapping of SOC stocks at various scales (e.g., Zhu et
al., 2001; Thompson et al., 2006; Adhikari et al., 2013).
Despite several global and regional studies on SOC inventories, quantitative
data on the relationship between SOC stocks and the environmental
controlling factors do not exist at multiple scales (Lal, 2004; Torn et al.,
2009; Chaplot et al., 2010). In the spatial prediction of SOC concentration and
stocks, different primary and secondary topographic attributes are
calculated from a digital elevation model (DEM) and used, along with other
soil-forming factors such as climate, land cover type, and parent material,
to predict SOC stocks across different scales (Hancock et al., 2010; Vasques
et al., 2010; Kumar et al., 2012). Usually, fine-scale environmental data
are preferred over coarser spatial scales as they are more representative of
natural landscapes. However, it has also been reported that the highest-scale DEMs do not always produce highest accuracy in predicting soil
properties and that knowledge of the appropriate DEM scale for a particular
landscape is important (Smith et al., 2006; Roecker and Thompson, 2010).
Calculated values of topographic indices of a study area differed depending
on the spatial scale of the DEM used (Wilson and Gallant, 2000; Thompson et
al., 2001; Kienzle, 2004). In a recent study, Vasques et al. (2012) showed
that the quality (R2) of predicted carbon stocks consistently decreased
with increasing grid size of the environmental data used by the models.
Information collected at one scale can be used to infer properties at either
smaller or larger scales (Beven, 1995), such as when using point observations
to estimate regional SOC stocks, or taking areal averages of SOC stocks from
ESMs and disaggregating them. The essence of successful scaling is to infer
the key patterns from information collected at one scale and use those
patterns to make inferences at another scale that maintain consistency in
the desired metrics across the scales (Western et al., 2002). We believe
that the statistical spatial structure of SOC stocks may be useful in (1) downscaling
and inferring fine-scale variability from coarse-scale ESM
predictions; (2) model benchmarking; and (3) developing reduced order model
formulations relating biogeochemical processes across scales. By model
benchmarking, we mean using observation-based scaling relationships to test
the land biogeochemical representations in Earth system models.
A large body of literature exists on spatial scaling of soil moisture, which is a
dominant control on SOC dynamics and stocks. Several studies have modeled
the spatial variability of soil moisture patterns from relatively smaller to
larger scales, and have attempted to characterize the spatial structure
based on system properties (Rodriguez-Iturbe et al., 1995; Peters-Lidard et
al., 2001; Western et al., 2002; Riley and Shen, 2014; Pau et al., 2014). For
some systems, soil moisture spatial variance follows a power law decay as a
function of spatial area (Manfreda et al., 2007), although in other systems
there are clear scale breaks in this relationship (e.g., Das and Mohanty,
2008; Joshi and Mohanty, 2010; Pau et al., 2014). Gebremichael et al. (2009)
reported that, in a watershed located in the southern Great Plains of the
USA, soil moisture showed scale invariance, and that if the scaling parameters
could be estimated from large-scale soil moisture fields, it might be
feasible to transform spatial soil moisture fields between scales. Despite
the progress made in modeling the scaling behavior of soil moisture, to our
knowledge no study exists that has examined the statistical structure of the
scaling behavior of SOC stocks.
Scaling approaches might also improve prediction of the spatial structure of
SOC stocks. The variogram, which relates the variance of SOC stock
differences between two points to the distance between the two points
(Webster and Oliver, 2007), is one approach to representing the spatial
structure of SOC stocks (Western et al., 2002). The main structural
parameters of a variogram are the nugget, sill, and range (Western and
Bloschl, 1999; Webster and Oliver, 2007). A nugget shows the unexplained
portion of the variance and the sill is the level at which a variogram
flattens and therefore represents the total variance of the variable. The
nugget-to-sill ratio can be used to quantify the percentage of overall
variance found at a distance smaller than the smallest lag interval, and to
classify the spatial dependence of soil properties (Cambardella et al.,
1994; Mora-Vallejo et al., 2008).
Current ESMs operate at spatial scales larger than 50 km and use a nested
subgrid hierarchy approach to represent the land surface heterogeneity
(Lawrence et al., 2012). ESM spatial scales are becoming increasingly finer
to more accurately represent the localized features of Earth systems that
affect energy, water, and greenhouse gas fluxes. For example, next-generation ESMs such as those being developed by the US Department of
Energy (Accelerated Climate Modeling for Energy; ACME) will have a spatial
scale for the land model of ∼ 10 km (Bader et al., 2014). In
this study, we successively increased the spatial scale (from s= 50 m to
10 km) of environmental variables and used observations and geospatial
approaches to predict SOC stocks. Throughout this paper, we refer to the
“scale” (s) as either the distance across which properties are assumed to be
homogeneous or the square root of the pixel area satisfying that criteria,
and note that the terms “scale” and “resolution” are often interchangeable
in this context. The idea was to model the change in predicted heterogeneity
of SOC stocks resulting from changing scale of the environmental data. In
this study, by the term “scaling” we mean the transfer of information
about environmental controls and statistical properties of SOC stocks from
one scale to another. We also investigated how environmental controls on SOC
stocks and the spatial structure of SOC stocks (the correlation length
(range), total variance (sill), and unstructured variability (nugget))
changed as a result of change in spatial scale of environmental variables.
Study approachSoil organic carbon observations and environmental variables
We used 556 georeferenced soil profile observations by combining data from
two recently published studies of soil organic carbon stocks across Alaska
(472 soil profiles from Mishra and Riley (2012) and 84 additional samples
from a recently published database of Michaelson et al., 2013). This
database combined the US Department of Agriculture National Resource
Conservation Service's pedons with the soil pedon observations collected
from the University of Alaska Fairbanks under its northern latitude soil
program (Michaelson et al., 2013). This database included measured
representative soil profiles from Alaska and covered all soil types at the
soil suborder level (18 suborders) and all 27 major land resource areas of
Alaska. The observed SOC stocks showed a wide range (0.35–296 kg m-2)
due to varying sampling depths (0.05–4.5 m depth), various soil types with
differing carbon content levels (Inceptisols to Gelisols), and the large
environmental heterogeneity present in the study area. About 50 % of the
observed samples were from the 0.05–1 m depth interval, 41 % of the
samples were from the 1–2 m depth interval, and the remaining samples
(9 %) were from the 2–4.5 m depth interval. A large number of
observations had SOC stocks ≤ 50 kg m-2, and about 49 samples had
SOC stocks greater than 100 kg m-2. A majority of pedons with high SOC
stocks were located in the Arctic region of Alaska, which contains areas with
soils impacted by cryoturbation, and the majority of pedons with lower SOC
stocks were located in interboreal and coastal rainforests. The SOC stock
data has a unimodal (kurtosis, K= 9.4) positively skewed distribution
(coefficient of skewness, S= 2), and is unevenly distributed throughout
Alaska (Fig. 1). The fine-scale (spatial scale, s= 50 m) spatially
heterogeneous SOC stock estimates have uncertainty, as described by the
prediction errors in Mishra and Riley (2012). However, that study indicated
that the SOC stock estimates have reasonable fidelity with the observations
withheld from the estimation procedure, and therefore we believe are
sufficiently accurate to be used in the scaling analyses described here. As
more data become available, the approaches described here to evaluate
spatial scaling controls can be readily re-applied.
The spatial distribution of observation sites, a histogram, and summary
statistics of observed SOC stocks across Alaska.
We collected environmental variables of the study area from various sources.
The topographic attributes were derived from a digital elevation model (DEM)
with a 50 m spatial scale (s= 50 m) obtained from the US Geological
Survey (USGS) database (Gesch et al., 2009). From the DEM, 13 topographic
attributes were calculated that have been reported to be useful predictors
of the SOC stocks across different environmental conditions using the
Spatial Analyst function of ArcGIS (ArcGIS version 10.2, Environmental
Systems Research Institute, Inc., Redlands, CA, USA).
Climate data for long-term (1961–1990) average annual temperature,
precipitation, potential evapotranspiration (PET), and summer shortwave
radiation were obtained from the Scenario Network for Alaska and Arctic
Planning (SNAP, 2014) database, with a spatial scale of s= 2 km.
Land cover data of 60 m spatial scale (s= 60 m) was extracted for Alaska
from the National Land Cover Database (NLCD) database (Homer et al., 2007).
In this study, to reduce the number of categorical variables with
potentially redundant information, we reclassified the 19 NLCD land cover
types found in Alaska into 9 major categories. Thus, developed open space,
low intensity, medium intensity, and high intensity were classified as a
developed category; deciduous, evergreen, and mixed forests were classified
as a forest category; dwarf scrub and shrub scrub were classified as a scrub
category; shrub, sedge, or moss were classified as a herbaceous category;
pasture and cultivated lands were classified as a cultivated category; and
woody and herbaceous wetlands were classified as a wetland category. In the
reclassified map, the category with the largest land area was the scrub
category (43 %), followed by forest (25 %), barren (8.5 %), herbaceous
(7 %), and wetlands (7 %). The remaining surface area (9.5 %) was
under open water, perennial ice, barren land, and moss vegetation. Indicator
variables for the presence or absence of seven land cover types (except open
water and perennial ice) were created and used in the model selection
process.
The surficial geology data of Alaska was obtained from a USGS database
(Karlstrom, 1964) in which the entire state of Alaska was classified into
27 different types of surficial geology. The category with the largest land
area was mountain alluvium and colluvium (22.5 %), followed by coarse
rubble (19 %), coastal alluvium (8.5 %), glacial moraine (7 %), and
undifferentiated mosaics (6 %). The remaining land area (37 %) was
placed in the remaining 22 surficial geology types.
Spatial scaling and environmental controls
We investigated changes in environmental controls on SOC stocks at spatial
scales of 100, 200, and 500 m and 1, 2, 5, and 10 km. For this
purpose, the DEM of a 50 m spatial scale was successively aggregated to
100, 200, and 500 m and 1, 2, 5, and 10 km using the bilinear
convolution algorithm of ArcGIS 10.2 (Fig. 2). Topographic attributes were
calculated at each spatial scale and included in predicting SOC stocks at
specific scales. The land cover types and surficial geology data were
aggregated at similar scales using the nearest-neighbors algorithm of ArcGIS
10.2 and were included in predicting SOC stocks at various spatial scales.
The spatial scaling approach used in this study. The black dot
represents the location of an SOC sampling site, and the rectangles denote
different pixel sizes of environmental variables (rectangles are not to scale).
Median values of the geographically weighted regression coefficients (β)
of log-transformed (natural log) SOC stock and environmental variables
(that were significant at all spatial scales) were calculated for each
spatial scale. Log transformations of SOC stocks were applied to meet the
linear regression assumptions of normality and constant variance of errors.
The change in the strength of environmental controls (β values) on SOC
stocks resulting from a change in spatial scale was investigated by plotting
the median values against the spatial scale at which they were calculated.
Several mathematical functions were used to represent the statistical nature
of scaling of the environmental controls on SOC stocks.
Selection of environmental predictors, prediction of SOC stocks,
and variogram modeling
We used best subset regression in SAS 9.3 (SAS Institute, 2011) to generate
all possible combinations of environmental variables to predict the SOC
stocks across Alaska. We used Mallows' Cp criterion to select three candidate
linear models for each spatial scale for which Cp values were close to the
number of predictors (Kutner et al., 2004; p. 358), from which we
subsequently selected one linear model for each spatial scale with
uncorrelated and statistically significant environmental predictors.
The presence of multicollinearity among selected environmental predictors was
tested by calculating the variance influence factors (VIFs) for each of the
selected variables. The VIFs for all the variables included in models
selected at different spatial resolutions were < 5. High levels of
multicollinearity (VIF > 10) can falsely inflate the least
squares estimates (Kutner et al., 2004; O'Brien, 2007; Gomez et al.,
2013). The selected environmental predictors were then used in a
geographically weighted regression approach (Mishra and Riley, 2012, 2014) to
predict the whole profile SOC stocks across Alaska at different spatial
scales using
Cui,vi=βoui,vi+∑i=1pβkui,viXk+εui,vi,
where C is the SOC stock at a certain location, uivi are the
geographical coordinates, Xk is the environmental predictor, p is
the number of independent variables, βo and
βk are the geographically weighted regression
coefficients, and ε is the error term. We used
adaptive kernel bandwidth in this study given that the sample density
varied over the study area. The optimal bandwidth was determined by
minimizing the corrected Akaike Information Criterion (AICc) as described in
Fotheringham et al. (2002).
We calculated several statistical parameters, including mean (μ),
variance (σ2), skewness (S), and kurtosis (K) from the predicted
SOC stocks at each specific spatial scale. The predicted variances were
plotted against spatial scale and a best-fit mathematical function was
determined. Relationships between the μ and other statistical
parameters were investigated by plotting the μ SOC stocks calculated at
each spatial scale across Alaska versus its other statistical parameters
calculated at the same scale.
To study the change in spatial structure of SOC stocks due to spatial
scaling, we calculated the SOC stock variograms (Webster and Oliver, 2007)
at different spatial scales:
γ(h)=12n∑i=1nZXi-Z(Xi+h)2,
where Z(Xi) and Z(Xi+h) are the measured SOC stocks at Xi and
Xi+h, respectively; h is the lag; n is the number of paired comparisons
at that lag; and γ(h) is the semivariance. By varying h in discrete
steps, we obtain an ordered set of semivariances (Webster and Oliver, 1992).
Suitable mathematical functions were fitted to the calculated semivariance
values using weighted least squares (Webster and Oliver, 2007). The best-fit
model parameters for each spatial scale are provided in Table 2. We examined
the change in correlation length (range), total variance of SOC stocks
(sill), and the unstructured variability (nugget) resulting from the change
in the spatial scales of environmental variables. A variable is considered
to have a strong spatial dependence if the nugget-to-sill ratio is less than
0.25; a moderate spatial dependence if the ratio is between 0.25 and 0.75;
and otherwise a weak spatial dependence (Cambardella et al., 1994;
Mora-Vallejo et al., 2008). The range, which is also referred as correlation
length, is the distance at which the sill is reached and represents the
maximum extent of the spatial correlation between predicted SOC stocks. The
change in the spatial structure of variability of SOC stocks was evaluated
using the nugget-to-sill ratio and the correlation length.
Control of environmental factors on SOC stocks as a function of
spatial scale. Each dot is a median geographically weighted regression
coefficient (β) for a particular spatial scale. The fitted functions
are (a) elevation β=-0.0009 + 0.0003 × (1 - exp(-0.0089 ×s),
adjusted R2= 0.83, P < 0.004, (b) temperature β=-0.11 + 0.037 × (1 - exp(-0.012 ×s),
adjusted R2= 0.94, P < 0.001, (c) potential evapotranspiration β= 0.066 + 0.187 × exp(-0.035 ×s),
adjusted R2= 0.97, P < 0.001, (d) scrub β= 0.395 - 0.0696 ×s, adjusted R2= 0.85, P < 0.001.
ResultsInferred environmental controls on SOC stocks change with scale
The set of significant environmental predictors and their individual
strengths varied with spatial scale. Statistically significant environmental
predictors at different spatial scales and the predicted variance of SOC
stocks are summarized in Table 1. From the 13 topographic attributes,
5 attributes – elevation (meters), slope (degree), aspect (degree from
north), soil wetness index (SWI), and sediment transport index (STI) – were
significant predictors of SOC stocks at various spatial scales. Among land
cover types, barren, scrub, herbaceous, and cultivated land covers were
significant predictors. Among different climatic factors, surface air
temperature and potential evapotranspiration were significant predictors.
Among surficial geology types, the glacial moraine, fluvial,
undifferentiated mosaic, coastal delta, and volcanic mountain types were
significant predictors at various spatial scales. Among all of the
environmental variables investigated in this study, only elevation,
temperature, potential evapotranspiration, and scrubland cover types were
significant predictors of SOC stocks at all spatial scales. In general, at
finer spatial scales, controls of topographic attributes were more
prominent, whereas land cover and surficial geology types were more
significant predictors at coarser scales (≥ 500 m spatial scale).
Fewer environmental variables controlled the variability of SOC stocks at
finer spatial scales, whereas the number of predictors increased at larger
spatial scales.
Environmental predictors and predicted variance of soil organic
carbon stocks across different spatial scales. Black dots represent
statistically significant (P < 0.05) predictors.
Our results showed that the strength of the control (median geographically
weighted regression coefficient across Alaska) of elevation on SOC stocks
decreased by 31 % as the spatial scale increased from 50 m to 1 km. Beyond
this scale, we found no change in the control of elevation on predicted SOC
stocks (Fig. 3a). The control of temperature on SOC stocks decreased with
spatial scale between 50 m and 500 m and became constant at larger scales
(Fig. 3b). The controls of elevation and temperature on SOC stocks across
spatial scales can be accurately modeled by using exponential functions with
R2= 0.83 and 0.94, respectively. The control of potential
evapotranspiration decreased by 36 % as the spatial scale increased from
50 m to 500 m, and became constant beyond 500 m (Fig. 3c). The control of
potential evapotranspiration on SOC stocks across spatial scales can be
modeled by using an exponential decay function (R2= 0.97). The control
of scrub vegetation (shrubs less than 5 m tall) on SOC stocks decreased
linearly (from 0.3 to 0.13) with scale over the range 50 m to 10 km (Fig. 3d).
At finer scales, scrub vegetation showed higher control on SOC stocks, which
decreased by about 57 % as the scale increased. Despite the observed
decrease in control of scrub vegetation on SOC stocks due to scaling, the
relationship between scrub vegetation and SOC stocks remained positive. The
control of scrub vegetation on SOC stocks can be modeled using a linear
function (R2= 0.85).
Modeled variogram parameters of predicted soil organic carbon
stocks at various spatial scales.
Spatial scale (m)Nugget (Ln kg m-2)2Sill (Ln kg m-2)2Nugget/sill (%)Range (km)500.120.452714841000.070.262710942000.040.2019.511265000.030.1618112410000.030.1519107820000.040.1721117050000.030.1620.5117410 0000.030.16191129Scaling impacts on the spatial structure of SOC stocks
The variogram summarizes the statistical structure of spatial variability
and is known as a summarizing function of the investigated property. For the
predicted SOC stocks, the variograms at finer scales showed significant
amount of unexplained variance (nugget) (Table 2) due to measurement errors
and/or microscale spatial heterogeneity not captured across the study area.
Both the nugget and sill decreased as the scale increased from finer to
coarser spatial scales. The nugget and sill decreased by 75 and 64 %,
respectively, as s increased from 50 m to 500 m and remained constant beyond
500 m scale (Fig. 4a). The relationship between these variogram parameters
and scale can be accurately described using exponential functions with
R2 of 0.98. The correlation length of SOC stocks remained relatively
constant up to about 1100–1400 km across spatial scales (Fig. 4b). The
nugget-to-sill ratio of predicted SOC stocks at the 50 and 100 m spatial
scales showed moderate spatial dependency (i.e., a nugget-to-sill ratio
> 25 %; Cambardella et al., 1994). However, strong, and
relatively similar, spatial dependency (a nugget-to-sill ratio ≤ 25 %)
was predicted for spatial scales between s= 200 m and s= 10 km
(18–21 %; Table 2). These results suggest that the predicted SOC stocks
show different spatial structure below s= 100 m as compared to s≥ 200 m.
Change of variogram parameters with scale (a), and calculated
variograms of log-transformed predicted SOC stocks (b) at spatial scales
of 50, 100, 200, and 500 m and 1, 2, 5, and 10 km. Fitted functions
are sill = 0.163 + 0.763 × exp(-0.0197 ×s), adjusted R2= 0.98,
P < 0.001; Nugget = 0.032 + 0.201 × exp(-0.016 ×s), adjusted
R2= 0.98), P < 0.001.
Statistical behavior of spatial scaling of SOC stocks
We found different statistical properties in predicted SOC stocks as the
spatial scale of environmental variables increased. The variance of
predicted SOC stocks decreased by 45 % as the scale increased from 50 to
500 m and remained constant beyond 500 m (Fig. 5). An exponential function
based on spatial scale accounted for 98 % of variability in the variance
of predicted SOC stocks across Alaska. These results suggest that the
spatial heterogeneity of SOC stocks decreases exponentially with scale until
about 500 m. Beyond this scale, no change in the spatial heterogeneity of
SOC stocks was predicted. The higher-order moments (skewness S and kurtosis K)
of the predicted SOC stocks decreased as the spatial scale increased
(Fig. 6a). S decreased from 1.4 to 0.8 as the scale increased from 50 to 200 m;
and fluctuated between 1.25 and 0.74 as the scale increased further. K
decreased from 5.7 to 3.6 as the scale increased from 50 to 200 m and
fluctuated between 5.1 and 3.68 beyond a scale of 200 m.
We evaluated the relationships of mean SOC stocks (μ) generated at each
spatial scale with σ2, S, and K. Within the investigated range of
μ SOC stocks (45.7 to 50.4 kg m-2), we found moderately accurate
linear relationships between μ and σ2, S, and K of predicted SOC
stocks, with R2 values of 0.59, 0.63, and 0.55, respectively (Fig. 6b–d).
Significant negative slopes of these relationships indicate that as
μ increases, the higher-order moments of SOC stock decrease, and therefore
the μ of SOC stocks can be used to predict SOC spatial heterogeneity.
Discussions
Soil organic carbon lies at the interface between the atmosphere and
pedosphere and can be altered at time scales relevant to climate change by
anthropogenic and climatic factors. As a result, the spatial heterogeneity
of SOC stocks may affect the magnitude of greenhouse gas fluxes from the
land surface and the terrestrial carbon cycle.
Several studies have demonstrated the impact of DEM scale on calculated
topographic attributes (Thompson et al., 2001; McMaster, 2002; Smith et al.,
2006; Roecker and Thompson, 2010). However, very little attention has been
paid to the impact of scaling on environmental controls and the predicted
spatial heterogeneity of soil properties. We found that apparent significant
environmental controllers of high-latitude SOC stocks changed with scale.
Our findings are consistent with the results of Vasques et al. (2012), who
showed inconsistent controls of various tropical system environmental
factors in predicting SOC stocks as the scale of environmental variables
increased from 30 to 1920 m. Due to a lack of other scaling studies
examining the change in environmental controllers of SOC stocks, we compared
our results with findings from two studies that reported environmental
controllers of SOC stocks at two different scales. Johnson et al. (2011)
reported that at the plot scale (∼ 1 m2), surface air
temperature, topographic attributes, and soil texture were primary
controllers of SOC stocks across Alaska. Similarly, Martin et al. (2011)
predicted SOC stocks at the 12 km scale over France, and reported land
use and clay content to be important drivers of SOC stock spatial
variability. Our results at the 50 m and 10 km scales are partially consistent
with these findings, showing significant controls of temperature, land cover
types, and topographic attributes on SOC stocks. Our results showed that the
strength of controls of environmental factors that were significant
decreased as spatial scale increased. The largest decrease was found in the
control of scrubland cover type, and the smallest decrease was found in the
control of temperature. The rates of these changes can be modeled using
simple mathematical functions.
The scaling properties of soil moisture have been widely studied (Western
and Boschl, 1999; Isham et al., 2005; Famiglietti et al., 2008; Li and
Rodell, 2013). Some studies reported that the variance of soil moisture
follows a power law relationship with surface area (Rodriguez-Iturbe et al.,
1995; Manfreda et al., 2007), while others have shown non-simple scaling
(Joshi and Mohanty, 2010; Riley and Shen, 2014; Pau et al., 2014). Beven
(1995) pointed out that it is unlikely that any general scaling theory can
be developed because of the dependence of hydrological systems on geological
perturbations, and advocated for a disaggregation approach to develop
scale-dependent models to represent hydrological heterogeneity. These
studies suggested that further work focusing on the factors influencing soil
moisture (topography, vegetation, soil properties, and rainfall) is expected
to increase understanding of the mechanisms affecting the scaling properties
of soil moisture.
Variance of soil organic carbon stocks as a function of spatial
scale. Each dot is predicted variance of SOC stock at each spatial scale
across Alaska. The fitted function is SOC variance = 260.61 + 422.42 × exp(-0.0318 ×s),
adjusted R2= 0.98, P < 0.001.
Keeping these inferences and that soil moisture is an important
control on SOC dynamics in mind, in this study we used the soil-forming factors that
have been documented to affect SOC stocks to study the spatial scaling
behavior of SOC stocks. However, in contrast to soil moisture, our results
show that the variance of SOC stocks follows an exponential decay with
spatial scale up to about 500 m, and then remains constant thereafter. We
interpreted environmental controllers on SOC stocks in an equilibrium sense;
i.e., over hundreds to thousands of years these controllers are expected to
be related to observed SOC stocks. However, transient responses are not
expected to follow the same scaling properties, given likely changes in
thermokarst formation and other hydrological and geomorphological changes at
high latitudes.
The spatial structure of SOC stocks results from the spatial structure of
soil-forming factors (Jenny, 1941; McBratney et al., 2003). Besides the
state factors described in the Introduction, SOC stocks of Alaska and other
arctic regions are also impacted by cryopedogenic features (pingos, frost
boils, hummocks) and thermal surface erosion resulting from the freezing and
thawing of the polygonal land surface (Tarnocai and Bockheim, 2011; Ping et
al., 2008; Ping, 2013). In this study, the spatial organization of predicted
SOC stocks increased with spatial scale as indicated by moderately lower
nugget-to-sill ratios for spatial scales > 200 m. However, the
correlation length remained relatively constant in the upscaled SOC stocks
across Alaska.
Higher-order moments of predicted SOC stocks as a function of
spatial scale (a), and relationships between predicted mean SOC stocks and
its (b) variance, (c) skewness, and (d) kurtosis within the range of
predicted mean values of SOC stocks.
One potential approach to represent the spatial heterogeneity of soil
properties in ESMs is to relate their statistical properties to the mean
state. As an analogy, several soil moisture studies investigated the
relationships between soil moisture mean and higher-order statistics, such
as σ2, S, and K (Famiglietti et al., 1999, 2008; Ryu and Flamiglietti,
2005; Li and Rodell, 2013). The results from these
studies suggest that the mean of soil moisture is often related to its
σ2, S, and K, although with different functional forms depending
on various system properties. Our results indicate a moderate but
statistically significant linear relationship between the mean and
higher-order moments of SOC stocks (i.e., σ2, S, and K decrease
linearly with the mean SOC stock within the range of mean SOC stocks
investigated in this study (45.5–50.4 kg m-2)). The strength of the
linear relationship was highest between μ and S (R2= 0.63,
P < 0.01), and lowest between μ and K (R2= 0.55,
P < 0.05). However, available observations are insufficient to
determine whether the same relationship holds with dynamically changing mean
SOC stocks, highlighting an area for further investigation.
Current land models integrated in ESMs, such as CLM4.5 (Lawrence et al.,
2012; Koven et al., 2013; Tang et al., 2013), use a nested subgrid hierarchy
approach to represent the land surface heterogeneity. In this approach the
grid cells (∼ 1 × 1∘) are divided into nonspatially
explicit land units (such as vegetated, lakes, urban, glacier, and crops),
columns (with variability in hydrological, snow, and crop management), and
plant functional types (accounting for variations in broad categories of
plants and bare ground). We have shown here that this type of representation
does not characterize the environmental controls and scaling properties of
SOC stocks; rectifying this problem would require substantial restructuring
of the model's subgrid hierarchy. One potential application of the
relationships we developed in this study could be to apply them with
coarse-resolution ESM results in order to generate fine-scale spatial
heterogeneity parameters of SOC stocks that are more representative of the
natural landscape. Currently the land models of most ESMs have a spatial
scale of ≥ 50 km. In the next 5–10 years, we believe ESM land models
will function much closer to the resolution we identify in our study as
being representative of the SOC landscape heterogeneity (∼ 10 km;
Bader et al., 2014). As the model resolution becomes finer in next-generation ESMs, data sets such as the one we describe in this study will be
critical for model benchmarking. We note that many environmental factors
that we found significant at various scales are not represented in current
land models. However, representing these factors in future land model
developments can improve our understanding of SOC dynamics of arctic/boreal
systems.
Median values of regression coefficients of different environmental controls
might change if a global or continental scale study would have been
conducted. Other environmental factors which are not significant predictors
of Alaskan SOC stocks might become significant in different study domains
such as in temperate and tropical ecosystems. Therefore extending this kind
of scaling study in larger spatial domains might produce more important
information for benchmarking ESM results. We note this as a limitation to our
study and recommend further studies to investigate these factors in other
systems and at larger spatial extents.
Soil texture has also been reported to be related to SOC stocks. To
investigate the use of soil texture in our scaling study, we collected the
soil texture data currently used in CLM 4.5 (Bonan et al., 2002) that was
available at ∼ 8 km spatial resolution across Alaska. However,
this data has approximately one soil texture value in each Alaska ecoregion
implying that the data must have been derived from a source with a much
coarser spatial resolution (International Geosphere-Biosphere Programme soil
data set that had 4931 soil mapping units globally; CLM 4.5 Technical notes).
Because of this limitation, we were unable to include soil texture in the
current scaling study. However, if soil texture information becomes
available at finer spatial scales, it could be readily incorporated in
future studies using the methods described here.
Summary and conclusions
Understanding the spatial scaling structure of SOC stocks and their
relationships with environmental factors is important for prediction of
carbon–climate feedbacks under a changing climate. Here, we estimated the
spatial scaling properties of environmental factors and statistical
properties of SOC stocks. We conclude that environmental controllers of SOC
stocks change with scale, and the strength of environmental controls can be
accurately modeled using simple mathematical functions. The variance of
predicted SOC stocks decreases exponentially with scale up to about 500 m,
and then remains constant thereafter. Our results showed that the mean
predicted SOC content is linearly related with its variance, skewness, and
kurtosis. If the objective of a study is to represent the spatial
heterogeneity of SOC stocks resulting from environmental factors, the
prediction spatial scale should be finer than ∼ 500 m.
Similarly, the choice of environmental predictors should be based on the
intended final spatial scale of predicted SOC stocks. Therefore, the current
subgrid structure of many ESM-scale land models does not allow for
characterization of the environmental controls and scaling properties
affecting SOC stocks. The findings of this study may help to develop
scale-appropriate techniques for ESM-scale land models and ultimately reduce
the existing uncertainties in carbon–climate feedback predictions.
Acknowledgements
This research was supported by the Director, Office of Science, Office of
Biological and Environmental Research of the US Department of Energy under
Argonne National Laboratory contract no. DE-AC02-06CH11357, and the Regional
and Global Climate Modeling (RGCM) Program. Contributions of W. J. Riley were
supported under Lawrence Berkeley National Laboratory contract no.
DE-AC02-05CH11231 as part of the RGCM program and the Next-Generation
Ecosystem Experiment Arctic project. Thanks to G. Michaelson and C. L. Ping
for providing access to some of the SOC profile data.
Edited by: S. Zaehle
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